We consider the rotating and translating equilibria of open finite vortex
sheets with endpoints in two-dimensional potential flows. New results are
obtained concerning the stability of these equilibrium configurations which
complement analogous results known for unbounded, periodic and circular vortex
sheets. First, we show that the rotating and translating equilibria of finite
vortex sheets are linearly unstable. However, while in the first case unstable
perturbations grow exponentially fast in time, the growth of such perturbations
in the second case is algebraic. In both cases the growth rates are increasing
functions of the wavenumbers of the perturbations. Remarkably, these stability
results are obtained entirely with analytical computations. Second, we obtain
and analyze equations describing the time evolution of a straight vortex sheet
in linear external fields. Third, it is demonstrated that the results
concerning the linear stability analysis of the rotating sheet are consistent
with the infinite-aspect-ratio limit of the stability results known for
Kirchhoff's ellipse (Love 1893; Mitchell & Rossi 2008) and that the solutions
we obtained accounting for the presence of external fields are also consistent
with the infinite-aspect-ratio limits of the analogous solutions known for
vortex patches.